# Word Problems - PowerPoint by rt3463df

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```									Test Topics
 Graph a sinusoid given equation in transformational form or
functional form
 State mapping rule
 Given the mapping rule, state the transformations
 Given the mapping rule, state equation in functional or
transformational form
 State transformations
 Given graph state equation as transformation of sine or cosine
 Given word problem graph and state equation
 State amplitude, period, phase shift, principal axis, local maximum,
local minimum
Transformational                                Functional
1 ( y VT ) sin 1  x  HT   y VS sin 1  x  HT   VT
                             
VS                       HS 





 HS 




1( y 6) sin 2 x 30             y  3sin 2 x 30 6







       
3               
                                
          


Transformations                     Rx  No
VT  6
VS  3
HS  1  period 180
2
HT  30
PA y  6
                         

Mapping Rule          

   x, y  1 x 30,3y 6









      
2




Word Problems
Ferris Wheel

A Ferris wheel has a diameter of 32 m,
and its centre is 18 m above the ground.
The wheel completes one revolution
every 30 seconds.
a)   Graph a rider’s height above the ground (m) versus
time (s) during a 2 minute ride. State any assumptions.
b)   Write an equation to model this relationship.
c)   State the domain and range of the function.
Principal Axis

A Ferris wheel has a diameter of 32 m, and its centre is
18 m above the ground. The wheel completes one
revolution every 30 seconds.
Amplitude – Vertical Stretch

A Ferris wheel has a diameter of 32 m, and its centre is
18 m above the ground. The wheel completes one
revolution every 30 seconds.
Period

A Ferris wheel has a diameter of 32 m, and its centre is
18 m above the ground. The wheel completes one
revolution every 30 seconds.
Horizontal Stretch

HS = period
360             A Ferris wheel has a diameter of 32
m, and its centre is 18 m above the
ground.

=   30/360       The wheel completes one
revolution every 30 seconds.

= 1/12
Transformations

Vertical Translation     (Principal Axis)
Vertical Stretch         (Amplitude)
Horizontal Stretch       (Period/360)
Horizontal Translation   (Phase Shift)
Reflection

Write your own equation and graph
Transformations

Vertical Translation     (18)
Vertical Stretch         (16)
Horizontal Stretch       (1/12)
Horizontal Translation   (0)
Reflection               (Yes)
Which equation do you choose?
  1 ( y 16)  sin  1  x
       
18                       
12     

  1 ( y 18)  cos(12 x)
16
1 ( y 18)  sin(12 x)
16

 1 ( y 18)  sin(12 x)
16
 1 ( y 18)  sin(12 x)
16
Which graph makes sense? Why?

  1 ( y 18)  cos(12 x)
16
Domain=?   Range =?
Domain=?       Range =?

Domain = {x єR, x≥0}

Range = {y єR, 2 ≤ y ≤ 34}
Ocean Cycles
 A point on the ocean rises and falls as waves
pass. Suppose that a wave passes every 4
s, and the height of each wave from the crest
to the trough is 0.5 m.
 Sketch a graph to model the height of the point
relative to its average height for a complete
cycle.
 Use exact values to write an equation of the
form h = a cos kt to model the height of the
point, h meters, relative to its average
height, as a function of time, t seconds.